/* -*- mode: C -*-  */
/* 
   IGraph library.
   Copyright (C) 2006-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard street, Cambridge, MA 02139 USA
   
   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2 of the License, or
   (at your option) any later version.
   
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
   
   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA 
   02110-1301 USA

*/

#include <igraph.h>

int check_flow(int errorinc,
	       const igraph_t *graph, igraph_real_t flow_value, 
	       const igraph_vector_t *flow, const igraph_vector_t *cut, 
	       const igraph_vector_t *partition,
	       const igraph_vector_t *partition2, 
	       long int source, long int target, 
	       const igraph_vector_t *capacity, 
	       igraph_bool_t print) {

  long int i, n=igraph_vcount(graph), m=igraph_ecount(graph);
  long int nc=igraph_vector_size(cut);
  igraph_vector_t inedges, outedges;
  igraph_bool_t directed=igraph_is_directed(graph);
  igraph_real_t cutsize;
  igraph_t graph_copy;
  igraph_matrix_t sp;

  if (print) {
    printf("flow value: %g\n", (double) flow_value);
    printf("flow: "); igraph_vector_print(flow);
    printf("first partition:  "); igraph_vector_print(partition);
    printf("second partition: "); igraph_vector_print(partition2);
    printf("edges in the cut: ");
    for (i=0; i<nc; i++) {
      long int edge=VECTOR(*cut)[i];
      long int from=IGRAPH_FROM(graph, edge);
      long int to  =IGRAPH_TO  (graph, edge);
      if (!directed && from > to) {
	igraph_integer_t tmp=from;
	from=to;
	to=tmp;
      }
      printf("%li-%li (%g), ", from, to, VECTOR(*capacity)[edge]);
    }
    printf("\n");
  }
  fflush(stdout);
        
  /* Always less than the capacity */
  for (i=0; i<m; i++) {
    if (VECTOR(*flow)[i] > VECTOR(*capacity)[i]) {
      return errorinc+3;
    }
  }
  
  /* What comes in goes out, but only in directed graphs, 
     there is no in and out in undirected ones...
   */
  if (igraph_is_directed(graph)) {
    igraph_vector_init(&inedges, 0);
    igraph_vector_init(&outedges, 0);

    for (i=0; i<n; i++) {
      long int n1, n2, j;
      igraph_real_t in_flow=0.0, out_flow=0.0;
      igraph_incident(graph, &inedges,  i, IGRAPH_IN);
      igraph_incident(graph, &outedges, i, IGRAPH_OUT);
      n1=igraph_vector_size(&inedges);
      n2=igraph_vector_size(&outedges);
      for (j=0; j<n1; j++) {
	long int e=VECTOR(inedges)[j];
	in_flow += VECTOR(*flow)[e];
      }
      for (j=0; j<n2; j++) {
	long int e=VECTOR(outedges)[j];
	out_flow += VECTOR(*flow)[e];
      }
      if (i == source) {
	if (in_flow > 0) { return errorinc+4; }
	if (out_flow != flow_value) { return errorinc+5; }
      } else if (i == target) {
	if (out_flow > 0) { return errorinc+6; }
	if (in_flow != flow_value) { return errorinc+7; }
	
      } else {
	if (in_flow != out_flow) { return errorinc+8; }
      }
    }
    
    igraph_vector_destroy(&inedges);
    igraph_vector_destroy(&outedges);
  }

  /* Check the minimum cut size*/
  for (i=0, cutsize=0.0; i<nc; i++) {
    long int edge=VECTOR(*cut)[i];
    cutsize += VECTOR(*capacity)[edge];
  }
  if (fabs(cutsize-flow_value) > 1e-14) { return errorinc+9; }

  /* Check that the cut indeed cuts */
  igraph_copy(&graph_copy, graph);
  igraph_delete_edges(&graph_copy, igraph_ess_vector(cut));
  igraph_matrix_init(&sp, 1, 1);
  igraph_shortest_paths(&graph_copy, &sp, /*from=*/ igraph_vss_1(source),
			/*to=*/ igraph_vss_1(target), IGRAPH_OUT);
  if (MATRIX(sp, 0, 0) != IGRAPH_INFINITY) { return errorinc+10; }
  igraph_matrix_destroy(&sp);
  igraph_destroy(&graph_copy);

  return 0;
}

int main() {
  
  igraph_t g;
  igraph_real_t flow_value;
  igraph_vector_t cut;
  igraph_vector_t capacity;
  igraph_vector_t partition, partition2;
  igraph_vector_t flow;
  long int i, n;
  igraph_integer_t source, target;
  FILE *infile;
  igraph_real_t flow_value2=0.0;
  int check;
  igraph_maxflow_stats_t stats;
  
  igraph_vector_init(&capacity, 0);

  /***************/
  infile=fopen("ak-4102.max", "r");
  igraph_read_graph_dimacs(&g, infile, 0, 0, &source, &target, &capacity,
  			   IGRAPH_DIRECTED);
  fclose(infile);

  igraph_vector_init(&cut, 0);
  igraph_vector_init(&partition, 0);
  igraph_vector_init(&partition2, 0);
  igraph_vector_init(&flow, 0);

  igraph_maxflow(&g, &flow_value, &flow, &cut, &partition,
		 &partition2, source, target, &capacity, &stats);

  if (flow_value != 8207) {
    return 1;
  }

  n=igraph_vector_size(&cut);
  for (i=0; i<n; i++) {
    long int e=VECTOR(cut)[i];
    flow_value2 += VECTOR(capacity)[e];
  }
  if (flow_value != flow_value2) {
    return 2;
  }

  /* Check the flow */
  if ( (check=check_flow(0, &g, flow_value, &flow, &cut, &partition,
			 &partition2, source, target, &capacity, 
			 /*print=*/ 0))) {
    return check;
  }

  igraph_destroy(&g);
  igraph_vector_destroy(&capacity);
  igraph_vector_destroy(&cut);
  igraph_vector_destroy(&partition);
  igraph_vector_destroy(&partition2);
  igraph_vector_destroy(&flow);

  /* ------------------------------------- */

  igraph_small(&g, 4, IGRAPH_UNDIRECTED,
	       0,1,0,2,1,2,1,3,2,3, -1);
  igraph_vector_init_int_end(&capacity, -1, 4,2,10,2,2, -1);
  igraph_vector_init(&cut, 0);
  igraph_vector_init(&partition, 0);
  igraph_vector_init(&partition2, 0);
  igraph_vector_init(&flow, 0);

  igraph_maxflow(&g, &flow_value, &flow, &cut, &partition, &partition2, 
		 /*source=*/ 0, /*target=*/ 3, &capacity, &stats);

  if ( (check=check_flow(20, &g, flow_value, &flow, &cut, &partition,
			 &partition2, 0, 3, &capacity, 
			 /*print=*/ 1))) {
    return check;
  }

  igraph_vector_destroy(&cut);
  igraph_vector_destroy(&partition2);
  igraph_vector_destroy(&partition);
  igraph_vector_destroy(&capacity);
  igraph_vector_destroy(&flow);
  igraph_destroy(&g);

  /* ------------------------------------- */

  igraph_small(&g, 6, IGRAPH_DIRECTED,
	       0,1,1,2,2,3, 0,5,5,4,4,3, 3,0, -1);
  igraph_vector_init_int_end(&capacity, -1, 3,1,2, 10,1,3, 2, -1);
  igraph_vector_init(&cut, 0);
  igraph_vector_init(&partition, 0);
  igraph_vector_init(&partition2, 0);
  igraph_vector_init(&flow, 0);

  igraph_maxflow(&g, &flow_value, &flow, &cut, &partition, &partition2, 
		 /*source=*/ 0, /*target=*/ 2, &capacity, &stats);

  if ( (check=check_flow(40, &g, flow_value, &flow, &cut, &partition,
			 &partition2, 0, 2, &capacity, 
			 /*print=*/ 1))) {
    return check;
  }

  igraph_vector_destroy(&cut);
  igraph_vector_destroy(&partition2);
  igraph_vector_destroy(&partition);
  igraph_vector_destroy(&capacity);
  igraph_vector_destroy(&flow);
  igraph_destroy(&g);

  return 0;
}
